集成于薄板的压电型随机振动能量收集器件优化设计

Optimal design of plate-based random vibration energy harvesting system

将压电薄膜粘贴于方形薄板表面即构成实用的振动能量收集器件,本文研究此类器件在受到宽带随机点激励作用时以平均输出功率最大为目标的优化设计问题,具体包括压电片布置位置和尺寸要求、最优负载电阻等.首先,导出机电耦合系统关于位移和输出电压的随机偏微分-积分方程组,通过模态分析技术消去空间项得到关于主坐标和电压的无限维随机常微分方程组.进而,由线性随机振动理论建立平均输出功率的解析表达,优化问题据此展开.研究表明:宽带激励作用时,压电片最优中心位置处于激励点及与之相应的3个对称点;在最优布置条件下,平均输出功率随压电片尺寸增加近于单调增加,而增速渐缓,据此可定义最优尺寸;在最优布置条件下,平均输出功率随外接电阻的变化有极值出现,可由此断定最优负载电阻.上述研究揭示了对称最优布置位置的存在性及输出功率对布置位置的敏感性,对平板型随机振动能量收集器件的优化设计有一定的指导意义.

Pasting piezoelectric thin films on a rectangular plate constitutes a practical vibration energy harvester. This manuscript investigates the optimal design of energy harvesters excited by wideband random point force with the objective to maximizing the mean output power, including the position of piezoelectric patch, the dimension and the load resistance. First, derive the stochastic partially differential-integral equations with respect to the displacement and output voltage, and then by eliminating the partial variables through modal expansion technique, the stochastic ordinary differential equation with infinite dimensions with respect to principal coordinates and voltage is derived. The analytical expression on the mean output power is derived through the linear random vibration theory, based on that the optimal design is discussed in detail. The analytical results show that as for the wideband excitation, the optimal positions of the piezoelectric patch include the self- and the symmetric positions of the exciting point. With the optimal position, the mean output power almost monotonically increases with the dimension of the piezoelectric patch and the increasing speed declines. The optimal dimension can be determined base on the above results. The optimal load resistance is derived by the existence of extreme value of the relation curve between the mean power and load resistance. This manuscript discloses the symmetry of the optimal position and the sensitivity of mean power on position of piezoelectric patch, and provides certain guidance for the design of thin plate-based vibration energy harvesters.